2005 10B 17 · AMC 10 Step by Step

AMC 10 Step by Step

2005 AMC 10BProblem 17P16-20~3 minPrint

Exponents, Logarithms & Radicals Substitute to simplify (u = x+1/x, shifting, scaling)Collapse a sum or product by cancellation

Suppose that $4^a = 5$ , $5^b = 6$ , $6^c = 7$ , and $7^d = 8$ . What is $a \cdot b\cdot c \cdot d$ ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.